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Preliminary results for electron cloud induced coupled bunch instability in DAFNE. T. Demma INFN-LNF Thanks to K. Ohmi (KEK) ECM’08 November, 20-21, 2008 CERN (Geneva) - PowerPoint PPT Presentation
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Preliminary results for electron cloud induced coupled bunch instability in DAFNE
T. Demma INFN-LNF
Thanks to K. Ohmi (KEK)
ECM’08November, 20-21, 2008
CERN (Geneva)
Work supported in part by the “Ministero degli Affari Esteri, Direzione Generale per la Promozione e la Cooperazione Culturale”
Plan of talk
• Electron cloud at DAFNE
• Electron cloud multi-bunch instability– Wake field– Tracking simulations
• Comparison with experiments
• Conclusions and outlook
Electron cloud at DAFNE
• e+ current limited to 1.2 A by strong horizontal instability
• Large positive tune shift with current in e+ ring, not seen in e- ring
• Instability depends on bunch current
• Instability strongly increases along the train
• Anomalous vacuum pressure rise has been oserved in e+ ring
• Solenoids installed in free field regions strongly reduce pressure but have no effect on the instability (see A. Drago talk)
• Instability sensitive to orbit in wiggler and bending magnets
• Main change for the 2003 was wiggler field modification
Typical measurments
•Growth rates depends on bunch current•Most unstable mode is always a slow frequency mode (-1 mode)
Linear theory of e-cloud induced multibunch instability [S.S. Win et al., Phys. Rev. ST-AB 8, 094401 (2005)]
The momentum kick can calculated numerically using the PEI-M code (K.Ohmi, KEK).
Under linearity and superposition assumption, the momentum kick experienced by bunch i when bunch j is displached can be written as:
Coupled bunch instability is characterized by the dispersion relation:
Bunches oscillate with a mode characterized by:
..
/
/
...
0
2
numbharmM
cmE
bppN
e
p
Simulation assumptions
• Electron cloud uniformly distributed along the ring
• Electrons in the arcs are assumed to move in a uniform vertical magnetic field
• Circular chambers
Input parameters for DAFNE simulationsBunch population Nb 2.1; 4.2 x1010
Number of bunches nb 120; 60
Missing bunches Ngap 0
Bunch spacing Lsep[m] 0.8;1.6
Bunch length σz [mm] 18
Bunch horizontal size σx [mm] 1.4
Bunch vertical size σy [mm] 0.05
Chamber Radius R [mm] 40
Hor./vert. beta function x[m]/y[m] 4.1/1.1
Hor./vert. betatron tune x/y5.1/5.17
Primary electron rate dλ/ds 0.0088
Photon Reflectivity R 100% (uniform)
Max. Secondary Emission Yeld Δmax 1.9
Energy at Max. SEY Εm [eV] 250
Vert. magnetic field Bz [T] 1.7
Instability caused by electrons in the DAFNE arcs
• Lsep= 0.8 m
• bunch 400 is hor. displaced (x0=5mm)
• Electron distribution
• Wake force
•Growth rate ~ 100 turn
Wake linearity
Linearity is satisfied up to no more than the 410th bunch
dx=5 mm
dx=10 mm
Tracking simulation
•Solve both equations of beam and electrons simultaneously, giving the transverse amplitude of each bunch as a function of time.
•Fourier transformation of the amplitudes gives a spectrum of the unstable mode, identified by peaks of the betatron sidebands.
y
x
ze+ bunches
Electron cloud
~m
K.Ohmi, PRE55,7550 (1997)
K.Ohmi, PAC97, pp1667.
Bunch train evolution
1.2 A in 60 equispaced bunches
bunch
x [m
]
Mode spectrum and growth rate
60 equispaced bunches
Beam current 1.2 A
Growth time ~ 100 turn
-1 mode (60-5-1=54)
e-cloud density evolution
Bunch train evolution
1.2 A in 120 equispaced bunches
x [m
]
bunch
Mode spectrum and growth rate
120 equispaced bunches
Beam current 1.2 A
Growth time ~ 100 turn
-1 mode (120-5-1=154)
Simulations vs measurments
Measurment Simulation
I[mA]/nb /T0I[mA]/nb /T0
1000/105 73 1200/120 100
750/105 56 900/120 95
500/105 100 600/120 130
Conclusions and oulook
• Coupled-bunch instability has been simulated using PEI-M for the DAFNE parameters
• Preliminary results are in qualitative agreement with grow-dump measurments
• Explore a wider range of beam and chamber parameters
• Compare the results with other codes (Ecloud, POSINST)
• Modify the code to include ellyptical boundaries